25 Reputation

17 years, 60 days

How is Maple able to arrive at an exact ...

@Mariusz Iwaniuk  You are correct.  Thanks for pointing that out. The equation should read,

int[y'(x)*(x^2)/[(x^2)-1,x] = (int[sqrt(y(x))])^(-2/3)

How does Maple arrive at an implicit so...

Equation := int(diff(y(x), x)*w(x), x) = 1/int(sqrt(y(x))*w(x), x)^(2/3);
Solution := 3/4*y(x)^(4/3) + int(2/3*y(x)^(5/6)/int(sqrt(y(x))*w(x), x)^(5/3), x) + _C1 = 0;
Again, the advice provided by 'odeadvisor', was to formulate the Equation to the form
y(x) = G(x,y'(x)), then utilize the 'patterns' method which I could not apply, therefore it is the missing steps between 'Equation' and 'Solution'

Sorry,

JJP

How does Maple arrive at an implicit sol...

Your advice is well taken - Thanks. Incorporating it, I will give it a second shot - I hope you will too. Equation := int(diff(y(x), x)*w(x), x) = 1/int(sqrt(y(x))*w(x), x)^(2/3); Solution := 3/4*y(x)^(4/3) + int(2/3*y(x)^(5/6)/int(sqrt(y(x))*w(x), x)^(5/3), x) + _C1 = 0; Again, the advice provided by 'odeadvisor', was to formulate the Equation to the form y(x) = G(x,y'(x)), then utilize the 'patterns' method which I could not apply, therefore it is the missing steps between 'Equation' and 'Solution' Thanks Again, JJP

A resistant integro -differential equati...

Corection: Sorry all, I left out an exponential factor on the left side of the equation.